Hello everyone, I hope this is not the wrong place to ask. I’ve just changed my bike’s brakes (caliper type mechanism) because one of the two cable jackets did this (the black part correctly stops at the brake lever but the central part is smaller and is able to enter the brake lever). After changing to a new one at the front, I tensioned the back one and it broke the same way after a few tests. Am I doing everything wrong? (The bike is really old and rusty but seems to me I can only upload 1 pic per post)
Edit: link to some more photos


The steel inner hose should stay inside the hose, when breaking it should rest against the barrel adjuster (top-left)
If the inner cable hose is able to push through the barrel, it means the hole in it is too large (or the cable and hose too thin!) but also that the hose is really shitty quality for breaking like this
I’d recommend starting with buying the cable hose somewhere else, and maybe check the barrel adjuster as well, it should only allow the cable through